If the projection of a straight line segment on the coordinate axes are `2,3,6` then the length of the segment is

Options

A. 5 unit
B. 7 unit
C. 11 unit
D. 49 unit

Answer

To find the length of the line segment given its projections on the coordinate axes, we can follow these steps:

### Step 1: Understand the projections
The projections of the line segment on the x, y, and z axes are given as 2, 3, and 6 respectively. This means:
- The projection on the x-axis is 2 units.
- The projection on the y-axis is 3 units.
- The projection on the z-axis is 6 units.

### Step 2: Use the formula for the length of the line segment
The length \( L \) of a line segment in 3D space can be calculated using the formula:
\[ L = \sqrt{(x^2 + y^2 + z^2)} \]
where \( x \), \( y \), and \( z \) are the projections on the x, y, and z axes respectively.

### Step 3: Substitute the values
Substituting the values of the projections into the formula:
\[ L = \sqrt{(2^2 + 3^2 + 6^2)} \]

### Step 4: Calculate the squares
Calculating the squares:
\[ 2^2 = 4, \quad 3^2 = 9, \quad 6^2 = 36 \]

### Step 5: Sum the squares
Now, sum these values:
\[ L = \sqrt{(4 + 9 + 36)} = \sqrt{49} \]

### Step 6: Take the square root
Finally, take the square root:
\[ L = 7 \]

### Conclusion
The length of the line segment is \( 7 \) units.

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